Integrated Case: Risk and Return

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  • Topic: Investment, Modern portfolio theory, Risk in finance
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Integrated Case

8-23

Merrill Finch Inc.

Risk and Return

Assume that you recently graduated with a major in finance. You just landed a job as a financial planner with Merrill Finch Inc., a large financial services corporation. Your first assignment is to invest $100,000 for a client. Because the funds are to be invested in a business at the end of 1 year, you have been instructed to plan for a 1-year holding period. Further, your boss has restricted you to the investment alternatives in the following table, shown with their probabilities and associated outcomes. (For now, disregard the items at the bottom of the data; you will fill in the blanks later.)

Returns on Alternative Investments
Estimated Rate of Return
State of the
Economy

Prob.

Recession
Below Avg.
Average
Above Avg.
Boom

0.1
0.2
0.4
0.2
0.1

r
r-hat ( ˆ )
Std. dev. ()
Coeff. of Var. (CV)
beta (b)

T-Bills
5.5%
5.5
5.5
5.5
5.5

High
Tech
-27.0%
-7.0
15.0
30.0
45.0

Collections
27.0%
13.0
0.0
-11.0
-21.0
1.0%

0.0

13.2
13.2
-0.87

U.S.
Rubber
6.0%a
-14.0
3.0
41.0
26.0
9.8%
18.8
1.9
0.88

Market
Portfolio

2-Stock
Portfolio

-17.0%
-3.0
10.0
25.0
38.0

0.0%
7.5
12.0

10.5%
15.2
1.4

3.4
0.5

a

Note that the estimated returns of U.S. Rubber do not always move in the same direction as the overall economy. For example, when the economy is below average, consumers purchase fewer tires than they would if the economy were stronger. However, if the economy is in a flat-out recession, a large number of consumers who were planning to purchase a new car may choose to wait and instead purchase new tires for the car they currently own. Under these circumstances, we would expect U.S. Rubber’s stock price to be higher if there was a recession than if the economy was just below average.

Chapter 8: Risk and Rates of Return

Integrated Case

1

Merrill Finch’s economic forecasting staff has developed probability estimates for the state of the economy; and its security analysts have developed a sophisticated computer program, which was used to estimate the rate of return on each alternative under each state of the economy. High Tech Inc. is an electronics firm, Collections Inc. collects past-due debts, and U.S. Rubber manufactures tires and various other rubber and plastics products. Merrill Finch also maintains a “market portfolio” that owns a market-weighted fraction of all publicly traded stocks; you can invest in that portfolio, and thus obtain average stock market results. Given the situation as described, answer the following questions. A.

(1) Why is the T-bill’s return independent of the state of the economy? Do T-bills promise a completely risk-free return? Explain.

Answer:

[Show S8-1 through S8-7 here.] The 5.5% T-bill return does not depend on the state of the economy because the Treasury must (and will) redeem the bills at par regardless of the state of the economy. The T-bills are risk-free in the default risk sense because the 5.5% return will be realized in all possible economic states. However, remember that this return is composed of the real risk-free rate, say 3%, plus an inflation premium, say 2.5%. Since there is uncertainty about inflation, it is unlikely that the realized real rate of return would equal the expected 3%. For example, if inflation averaged 3.5% over the year, then the realized real return would only be 5.5% – 3.5% = 2%, not the expected 3%. Thus, in terms of purchasing power, T-bills are not riskless.

Also, if you invested in a portfolio of T-bills, and rates then declined, your nominal income would fall; that is, T-bills are exposed to reinvestment rate risk. So, we conclude that there are no truly riskfree securities in the United States. If the Treasury sold inflation-

2

Integrated Case

Chapter 8: Risk and Rates of Return

indexed, tax-exempt bonds, they would be truly riskless, but all actual securities...
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